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A Nearly Exact Discretization Scheme for the FitzHugh–Nagumo Model

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Abstract

In this paper, we apply the nearly exact discretization schemes to propose a discrete model for the FitzHugh–Nagumo model. We show that the discrete model obtained preserves the dynamics and the known features of the continuous FitzHugh–Nagumo model. We do so by performing distance-based and probability-based similarity analysis. Additionally, a sensitivity analysis is also performed to analyze the most influential parameters of the discrete system.

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Authors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Eddy Kwessi

  2. Department of Biostatistics, University of Alabama at Birmingham, Birmingham, AL, USA

    Lloyd J. Edwards

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  1. Eddy Kwessi
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  2. Lloyd J. Edwards
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Correspondence to Eddy Kwessi.

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Appendix

Appendix

Appendix A: Supplemental Figures for Similarity Analysis

See Fig. 13.

Fig. 13
figure 13

This figure shows the trajectory (red) of the CFHN model for parameters \(x_0=0, y_0=1, \epsilon =0.5, \gamma =0.5, a=1, I=1\), and \(T=25\). The green dashed lines represent the trajectories of the DFHN for the same parameters and for 100 values of \(\tau \), equally spaced between 0.005 and 0.3 (color figure online)

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Appendix B: Supplemental Figures for Sensitivity Analysis

See Fig. 14.

Fig. 14
figure 14

a and b show the evolution of total indices from t1 to t100 for outputs \(x_{t+1}\) and \(y_{t+1}\)

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Kwessi, E., Edwards, L.J. A Nearly Exact Discretization Scheme for the FitzHugh–Nagumo Model. Differ Equ Dyn Syst 32, 253–275 (2024). https://doi.org/10.1007/s12591-021-00569-5

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